Forecasting the Unseen: A Stationary Distribution Approach to Earthquake Magnitude Prediction in Bengkulu

Tubagus Robbi Megantara; Rizki Apriva Hidayana

doi:10.47194/ijgor.v6i2.379

Authors

Tubagus Robbi Megantara
tubagusrobbi@gmail.com
Department of Mathematics, Faculty of Mathematics and Natural Sceinces, National University of the Republic of Indonesia, Bandung, Indonesia
Rizki Apriva Hidayana

Keywords:

earthquake magnitude prediction, stationary distribution, markov chain, seismic hazard assessment, Bengkulu, probabilistic modeling, long-term forecasting

Abstract

Long-term forecasting of earthquake magnitudes plays a vital role in seismic hazard assessment and disaster mitigation, particularly in highly active seismic regions such as Bengkulu, Indonesia. This study introduces a probabilistic framework based on the stationary distribution of discrete-time Markov chains to predict the likelihood of various earthquake magnitudes over an extended period. Historical earthquake records from Bengkulu are categorized into discrete magnitude classes to form the states of the Markov chain. Transition probabilities between these states are estimated from the data, allowing for the construction of a transition matrix that accurately reflects the temporal dynamics of seismic activity. By analyzing the stationary distribution of this Markov chain, we derive the long-term probabilities of occurrence for each magnitude class, revealing inherent patterns in earthquake magnitudes that are otherwise difficult to capture with traditional methods. The stationary distribution serves as a stable, time-independent descriptor of the seismic regime, providing insights into the expected distribution of earthquake magnitudes in the future. The results indicate that this approach not only captures the probabilistic behaviour of seismic magnitudes but also offers a computationally efficient and interpretable model for earthquake forecasting. This modelling technique complements existing seismic hazard assessments and has practical implications for risk management and emergency preparedness in Bengkulu and other seismically active areas. Future research will explore the integration of spatial factors and earthquake depth to further enhance prediction accuracy.

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